On approximating the resolvent of a rotated Hamiltonian in the scattering region

We show that, with certain restrictions on the potentials, the Bubnov–Galerkin method enables one to approximate the resolvent of a two-body rotated Hamiltonian in the strong sense. In the general N-body case we find that one might encounter some spurious singularities. However, we suggest a slight modification in the method that enables one to construct a sequence that converges strongly to the exact resolvent. This provides a procedure to approximate the scattering amplitudes for all N-body collisions.